On the second largest multiplicity of eigenvalues for the Stieltjes string spectral problem on trees. (English) Zbl 1524.39025
Summary: The largest possible multiplicity of an eigenvalue of a spectral problem generated by the Stieltjes string equations on a metric tree is \(p_{pen}-1\), where \(p_{pen}\) is the number of pendant vertices. We propose how to find the second largest possible multiplicity of an eigenvalue of such a problem. This multiplicity depends on the numbers of point masses on the edges of the trees.
MSC:
39A27 | Boundary value problems for difference equations |
39A70 | Difference operators |
70F17 | Inverse problems for systems of particles |
70J30 | Free motions in linear vibration theory |